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# Conservation of Momentum in One Dimension

## Use conservation of momentum to solve collision problems in one dimension

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Derailing Trains

### Derailing Trains

Credit: Jeramey Jannene
Source: http://www.flickr.com/photos/37171504@N00/2467837785

The derailer pictured above is used to prevent out-of-control trains from colliding with other objects. While derailed trains take considerable energy to restore, the damage from two trains colliding is far worse.

#### Amazing But True

Credit: Son of Groucho
Source: http://www.flickr.com/photos/23401669@N00/1558798578

In order for a train to come to a complete stop, it must decelerate over a long distance [Figure2]

• Trains on average weigh between 8,000 to 10,000 tons and travel approximately 40 mph or 17.9 m/s. The average train would have a momentum between 143,200 ? 179,000 ton*m/s as it travels.
• Stopping an object smoothly and safely with such a magnitude would require a distance of at least a mile. Therefore, even if the conductor of a train was able to see a danger on the track ahead, he would be unable to stop the train in time.
• The limitation on stopping the train is because of friction and impulse. For a given frictional force applied to the train, a certain amount of time must pass for the final velocity to be brought to zero.

p=Ft\begin{align*}\triangle p=Ft\end{align*}

• Since there is a limit to the amount of force that can be applied to the train due to the brake or track, the only other possible method is to remove the train from the tracks completely.
• By using a derailer, the frictional force that is being applied to the train is increased by causing it to slide along the ground instead of the rails. Since more of the train will be in contact with the ground, a greater resistive force would be applied.

#### Explore More

Using the information provided above, answer the following questions.

1. If you were to a derail an 8,000,000 kg train that is traveling 10 m/s, how long will it take to bring it to a stop if a 2 kN frictional force is applied?
2. What is the major disadvantage of using a derailer?
3. Why is using a derailer safer than just erecting a several foot thick brick wall?

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